What you do:

Drain the mushrooms in a strainer, reserving the soaking liquid. Rinse the mushrooms thoroughly with cold water, then drain. Coarsely chop and set aside. Line the strainer with a coffee filter or paper towel and strain the soaking liquid; set aside.

In a large nonstick skillet, heat 1 tablespoon of the oil over medium-low heat. Cook the onion until slightly softened, stirring, about 3 minutes. Add half the garlic and increase the heat to medium. Cook, stirring, for 1 minute. Add the button mushrooms and cook, stirring, for 2 minutes, or until the mushrooms begin to give off their own liquid. Add the porcini mushrooms, their strained soaking liquid, wine, tomato paste, rosemary, salt, and pepper. Bring to a boil over medium-high heat. Reduce the heat to medium and cook, uncovered, stirring occasionally, until the liquids are almost completely reduced, about 20 minutes. Set aside.

Preheat the oven to 375 degrees. Lightly oil a 10- or 11-inch pie plate; set aside. In a medium stockpot placed on a back burner (the polenta tends to sputter), bring the water and broth to a boil over high heat. Slowly add the polenta, stirring constantly with a long-handled wooden spoon. Reduce the heat to low and stir in 2 tablespoons of the remaining oil, remaining garlic, and salt. Cover and cook, stirring occasionally, until tender and thickened, about 15 minutes. Remove from the heat and let stand, covered, for 5 minutes.

Immediately spoon half the polenta into the prepared pie plate, pressing down with the back of a large spoon to form a smooth surface. Spoon the mushroom filling on top, spreading to within a 1/2-inch of the outside edge of the polenta. Carefully spoon the remaining polenta over the filling, using your fingers to evenly spread and the back of a large spoon to form a smooth surface. Brush the top evenly with the remaining 1 teaspoon oil.

Cover with foil and bake for 30 minutes. Remove the foil and bake for 15 minutes, or until the top is lightly browned. Remove from the oven and let rest for 15 minutes. Cut into wedges and transfer to warmed serving plates. Spoon 1/3 cup warm pasta sauce over each serving. Garnish with the rosemary or parsley, if desired. Serve at once.